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    Area of Science:

    • Control Engineering
    • Computational Neuroscience
    • Applied Mathematics

    Background:

    • Delayed neural networks (DNNs) are crucial in modeling complex systems but pose challenges in stability analysis due to time delays.
    • Existing methods often struggle to fully exploit available information, limiting the precision of stability criteria.

    Purpose of the Study:

    • To develop an improved stability analysis method for delayed neural networks (DNNs).
    • To enhance existing stability criteria by incorporating additional degrees of freedom and information from extra states.

    Main Methods:

    • Development of improved delay-product type auxiliary polynomial-based functions (APFs).
    • Construction of a novel Lyapunov-Krasovskii functional incorporating APFs and integrals of quadratic forms.
    • Derivation of a new stability criterion that fully integrates improved inequalities and delay information.

    Main Results:

    • The proposed approach effectively exploits additional degrees of freedom and information on extra states.
    • The novel stability criterion reflects both the delay and its derivative, leading to more precise analysis.
    • Numerical examples demonstrate superior performance compared to existing methods.

    Conclusions:

    • The developed auxiliary polynomial-based functions (APFs) offer a more effective approach to stability analysis in delayed neural networks (DNNs).
    • The proposed method provides a more desirable performance by fully integrating advanced mathematical tools and information.
    • This work contributes to the robust design and analysis of complex dynamical systems involving time delays.